Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,3,Mod(433,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.433");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.bh (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.6185790339\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.577 |
Dual form | 720.3.bh.e.433.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | + | 7.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.0000 | 0.909091 | 0.454545 | − | 0.890724i | \(-0.349802\pi\) | ||||
0.454545 | + | 0.890724i | \(0.349802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.00000 | − | 9.00000i | 0.692308 | − | 0.692308i | −0.270432 | − | 0.962739i | \(-0.587166\pi\) |
0.962739 | + | 0.270432i | \(0.0871664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.00000i | −0.0588235 | − | 0.0588235i | 0.677083 | − | 0.735907i | \(-0.263244\pi\) |
−0.735907 | + | 0.677083i | \(0.763244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000i | 0.421053i | 0.977588 | + | 0.210526i | \(0.0675178\pi\) | ||||
−0.977588 | + | 0.210526i | \(0.932482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | + | 23.0000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000i | 0.275862i | 0.990442 | + | 0.137931i | \(0.0440452\pi\) | ||||
−0.990442 | + | 0.137931i | \(0.955955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.0000 | 0.451613 | 0.225806 | − | 0.974172i | \(-0.427498\pi\) | ||||
0.225806 | + | 0.974172i | \(0.427498\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 49.0000 | − | 7.00000i | 1.40000 | − | 0.200000i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 33.0000 | + | 33.0000i | 0.891892 | + | 0.891892i | 0.994701 | − | 0.102809i | \(-0.0327831\pi\) |
−0.102809 | + | 0.994701i | \(0.532783\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.0000 | 0.341463 | 0.170732 | − | 0.985318i | \(-0.445387\pi\) | ||||
0.170732 | + | 0.985318i | \(0.445387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15.0000 | − | 15.0000i | 0.348837 | − | 0.348837i | −0.510839 | − | 0.859676i | \(-0.670665\pi\) |
0.859676 | + | 0.510839i | \(0.170665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −39.0000 | − | 39.0000i | −0.829787 | − | 0.829787i | 0.157700 | − | 0.987487i | \(-0.449592\pi\) |
−0.987487 | + | 0.157700i | \(0.949592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.00000 | − | 7.00000i | 0.132075 | − | 0.132075i | −0.637979 | − | 0.770054i | \(-0.720229\pi\) |
0.770054 | + | 0.637979i | \(0.220229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.0000 | − | 40.0000i | 0.545455 | − | 0.727273i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 56.0000i | − | 0.949153i | −0.880214 | − | 0.474576i | \(-0.842601\pi\) | ||
0.880214 | − | 0.474576i | \(-0.157399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42.0000 | 0.688525 | 0.344262 | − | 0.938874i | \(-0.388129\pi\) | ||||
0.344262 | + | 0.938874i | \(0.388129\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.00000 | − | 63.0000i | −0.138462 | − | 0.969231i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | + | 7.00000i | 0.104478 | + | 0.104478i | 0.757413 | − | 0.652936i | \(-0.226463\pi\) |
−0.652936 | + | 0.757413i | \(0.726463\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 98.0000 | 1.38028 | 0.690141 | − | 0.723675i | \(-0.257549\pi\) | ||||
0.690141 | + | 0.723675i | \(0.257549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 49.0000 | − | 49.0000i | 0.671233 | − | 0.671233i | −0.286767 | − | 0.958000i | \(-0.592581\pi\) |
0.958000 | + | 0.286767i | \(0.0925807\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 70.0000 | + | 70.0000i | 0.909091 | + | 0.909091i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 96.0000i | − | 1.21519i | −0.794247 | − | 0.607595i | \(-0.792134\pi\) | ||
0.794247 | − | 0.607595i | \(-0.207866\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −63.0000 | + | 63.0000i | −0.759036 | + | 0.759036i | −0.976147 | − | 0.217111i | \(-0.930337\pi\) |
0.217111 | + | 0.976147i | \(0.430337\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00000 | + | 1.00000i | −0.0823529 | + | 0.0117647i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 112.000i | 1.25843i | 0.777233 | + | 0.629213i | \(0.216623\pi\) | ||||
−0.777233 | + | 0.629213i | \(0.783377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 126.000 | 1.38462 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.0000 | + | 24.0000i | 0.336842 | + | 0.252632i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 33.0000 | + | 33.0000i | 0.340206 | + | 0.340206i | 0.856445 | − | 0.516239i | \(-0.172668\pi\) |
−0.516239 | + | 0.856445i | \(0.672668\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −26.0000 | −0.257426 | −0.128713 | − | 0.991682i | \(-0.541085\pi\) | ||||
−0.128713 | + | 0.991682i | \(0.541085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −73.0000 | + | 73.0000i | −0.708738 | + | 0.708738i | −0.966270 | − | 0.257532i | \(-0.917091\pi\) |
0.257532 | + | 0.966270i | \(0.417091\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 121.000 | + | 121.000i | 1.13084 | + | 1.13084i | 0.990038 | + | 0.140804i | \(0.0449686\pi\) |
0.140804 | + | 0.990038i | \(0.455031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 136.000i | − | 1.24771i | −0.781542 | − | 0.623853i | \(-0.785566\pi\) | ||
0.781542 | − | 0.623853i | \(-0.214434\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 127.000 | − | 127.000i | 1.12389 | − | 1.12389i | 0.132743 | − | 0.991150i | \(-0.457621\pi\) |
0.991150 | − | 0.132743i | \(-0.0423786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.0000 | + | 161.000i | 0.200000 | + | 1.40000i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 14.0000i | − | 0.117647i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −0.173554 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −117.000 | − | 44.0000i | −0.936000 | − | 0.352000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000 | + | 7.00000i | 0.0551181 | + | 0.0551181i | 0.734129 | − | 0.679010i | \(-0.237591\pi\) |
−0.679010 | + | 0.734129i | \(0.737591\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −230.000 | −1.75573 | −0.877863 | − | 0.478913i | \(-0.841031\pi\) | ||||
−0.877863 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −56.0000 | + | 56.0000i | −0.421053 | + | 0.421053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 63.0000 | + | 63.0000i | 0.459854 | + | 0.459854i | 0.898607 | − | 0.438753i | \(-0.144580\pi\) |
−0.438753 | + | 0.898607i | \(0.644580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 88.0000i | 0.633094i | 0.948577 | + | 0.316547i | \(0.102523\pi\) | ||||
−0.948577 | + | 0.316547i | \(0.897477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 90.0000 | − | 90.0000i | 0.629371 | − | 0.629371i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32.0000 | + | 24.0000i | 0.220690 | + | 0.165517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 168.000i | − | 1.12752i | −0.825940 | − | 0.563758i | \(-0.809355\pi\) | ||
0.825940 | − | 0.563758i | \(-0.190645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −130.000 | −0.860927 | −0.430464 | − | 0.902608i | \(-0.641650\pi\) | ||||
−0.430464 | + | 0.902608i | \(0.641650\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.0000 | − | 56.0000i | 0.270968 | − | 0.361290i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −63.0000 | − | 63.0000i | −0.401274 | − | 0.401274i | 0.477408 | − | 0.878682i | \(-0.341576\pi\) |
−0.878682 | + | 0.477408i | \(0.841576\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −322.000 | −2.00000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −65.0000 | + | 65.0000i | −0.398773 | + | 0.398773i | −0.877800 | − | 0.479027i | \(-0.840990\pi\) |
0.479027 | + | 0.877800i | \(0.340990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −103.000 | − | 103.000i | −0.616766 | − | 0.616766i | 0.327934 | − | 0.944701i | \(-0.393648\pi\) |
−0.944701 | + | 0.327934i | \(0.893648\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000i | 0.0414201i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −73.0000 | + | 73.0000i | −0.421965 | + | 0.421965i | −0.885880 | − | 0.463915i | \(-0.846444\pi\) |
0.463915 | + | 0.885880i | \(0.346444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 119.000 | − | 217.000i | 0.680000 | − | 1.24000i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 56.0000i | 0.312849i | 0.987690 | + | 0.156425i | \(0.0499968\pi\) | ||||
−0.987690 | + | 0.156425i | \(0.950003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −70.0000 | −0.386740 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 231.000 | − | 33.0000i | 1.24865 | − | 0.178378i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0000 | − | 10.0000i | −0.0534759 | − | 0.0534759i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −142.000 | −0.743455 | −0.371728 | − | 0.928342i | \(-0.621235\pi\) | ||||
−0.371728 | + | 0.928342i | \(0.621235\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −63.0000 | + | 63.0000i | −0.326425 | + | 0.326425i | −0.851225 | − | 0.524800i | \(-0.824140\pi\) |
0.524800 | + | 0.851225i | \(0.324140\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 63.0000 | + | 63.0000i | 0.319797 | + | 0.319797i | 0.848689 | − | 0.528892i | \(-0.177392\pi\) |
−0.528892 | + | 0.848689i | \(0.677392\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 336.000i | − | 1.68844i | −0.535995 | − | 0.844221i | \(-0.680063\pi\) | ||
0.535995 | − | 0.844221i | \(-0.319937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −56.0000 | + | 56.0000i | −0.275862 | + | 0.275862i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 42.0000 | − | 56.0000i | 0.204878 | − | 0.273171i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 80.0000i | 0.382775i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −314.000 | −1.48815 | −0.744076 | − | 0.668095i | \(-0.767110\pi\) | ||||
−0.744076 | + | 0.668095i | \(0.767110\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.0000 | − | 105.000i | −0.0697674 | − | 0.488372i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 98.0000 | + | 98.0000i | 0.451613 | + | 0.451613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | −0.0814480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 135.000 | − | 135.000i | 0.605381 | − | 0.605381i | −0.336354 | − | 0.941736i | \(-0.609194\pi\) |
0.941736 | + | 0.336354i | \(0.109194\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 281.000 | + | 281.000i | 1.23789 | + | 1.23789i | 0.960864 | + | 0.277022i | \(0.0893474\pi\) |
0.277022 | + | 0.960864i | \(0.410653\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 168.000i | 0.733624i | 0.930295 | + | 0.366812i | \(0.119551\pi\) | ||||
−0.930295 | + | 0.366812i | \(0.880449\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −273.000 | + | 273.000i | −1.17167 | + | 1.17167i | −0.189863 | + | 0.981811i | \(0.560804\pi\) |
−0.981811 | + | 0.189863i | \(0.939196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −273.000 | + | 39.0000i | −1.16170 | + | 0.165957i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 288.000i | − | 1.20502i | −0.798111 | − | 0.602510i | \(-0.794167\pi\) | ||
0.798111 | − | 0.602510i | \(-0.205833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −446.000 | −1.85062 | −0.925311 | − | 0.379209i | \(-0.876196\pi\) | ||||
−0.925311 | + | 0.379209i | \(0.876196\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 196.000 | + | 147.000i | 0.800000 | + | 0.600000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72.0000 | + | 72.0000i | 0.291498 | + | 0.291498i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −150.000 | −0.597610 | −0.298805 | − | 0.954314i | \(-0.596588\pi\) | ||||
−0.298805 | + | 0.954314i | \(0.596588\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −230.000 | + | 230.000i | −0.909091 | + | 0.909091i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −161.000 | − | 161.000i | −0.626459 | − | 0.626459i | 0.320716 | − | 0.947175i | \(-0.396076\pi\) |
−0.947175 | + | 0.320716i | \(0.896076\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 462.000i | 1.78378i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −151.000 | + | 151.000i | −0.574144 | + | 0.574144i | −0.933284 | − | 0.359139i | \(-0.883070\pi\) |
0.359139 | + | 0.933284i | \(0.383070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.00000 | − | 49.0000i | −0.0264151 | − | 0.184906i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 376.000i | − | 1.39777i | −0.715234 | − | 0.698885i | \(-0.753680\pi\) | ||
0.715234 | − | 0.698885i | \(-0.246320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −210.000 | −0.774908 | −0.387454 | − | 0.921889i | \(-0.626645\pi\) | ||||
−0.387454 | + | 0.921889i | \(0.626645\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −70.0000 | − | 240.000i | −0.254545 | − | 0.872727i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 129.000 | + | 129.000i | 0.465704 | + | 0.465704i | 0.900520 | − | 0.434816i | \(-0.143186\pi\) |
−0.434816 | + | 0.900520i | \(0.643186\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 174.000 | 0.619217 | 0.309609 | − | 0.950864i | \(-0.399802\pi\) | ||||
0.309609 | + | 0.950864i | \(0.399802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −113.000 | + | 113.000i | −0.399293 | + | 0.399293i | −0.877984 | − | 0.478690i | \(-0.841112\pi\) |
0.478690 | + | 0.877984i | \(0.341112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 98.0000 | + | 98.0000i | 0.341463 | + | 0.341463i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 287.000i | − | 0.993080i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −345.000 | + | 345.000i | −1.17747 | + | 1.17747i | −0.197089 | + | 0.980386i | \(0.563149\pi\) |
−0.980386 | + | 0.197089i | \(0.936851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −224.000 | − | 168.000i | −0.759322 | − | 0.569492i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 414.000i | 1.38462i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 210.000 | 0.697674 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 126.000 | − | 168.000i | 0.413115 | − | 0.550820i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 327.000 | + | 327.000i | 1.06515 | + | 1.06515i | 0.997725 | + | 0.0674220i | \(0.0214774\pi\) |
0.0674220 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.00000 | 0.00643087 | 0.00321543 | − | 0.999995i | \(-0.498976\pi\) | ||||
0.00321543 | + | 0.999995i | \(0.498976\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 81.0000 | − | 81.0000i | 0.258786 | − | 0.258786i | −0.565774 | − | 0.824560i | \(-0.691423\pi\) |
0.824560 | + | 0.565774i | \(0.191423\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 159.000 | + | 159.000i | 0.501577 | + | 0.501577i | 0.911928 | − | 0.410351i | \(-0.134594\pi\) |
−0.410351 | + | 0.911928i | \(0.634594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 80.0000i | 0.250784i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | − | 8.00000i | 0.0247678 | − | 0.0247678i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −279.000 | − | 153.000i | −0.858462 | − | 0.470769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 546.000i | − | 1.65957i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 182.000 | 0.549849 | 0.274924 | − | 0.961466i | \(-0.411347\pi\) | ||||
0.274924 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 49.0000 | − | 7.00000i | 0.146269 | − | 0.0208955i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −447.000 | − | 447.000i | −1.32641 | − | 1.32641i | −0.908479 | − | 0.417930i | \(-0.862756\pi\) |
−0.417930 | − | 0.908479i | \(-0.637244\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 140.000 | 0.410557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.0000 | + | 25.0000i | 0.0720461 | + | 0.0720461i | 0.742212 | − | 0.670166i | \(-0.233777\pi\) |
−0.670166 | + | 0.742212i | \(0.733777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 200.000i | − | 0.573066i | −0.958070 | − | 0.286533i | \(-0.907497\pi\) | ||
0.958070 | − | 0.286533i | \(-0.0925028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −321.000 | + | 321.000i | −0.909348 | + | 0.909348i | −0.996220 | − | 0.0868711i | \(-0.972313\pi\) |
0.0868711 | + | 0.996220i | \(0.472313\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 294.000 | − | 392.000i | 0.828169 | − | 1.10423i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 112.000i | − | 0.311978i | −0.987759 | − | 0.155989i | \(-0.950144\pi\) | ||
0.987759 | − | 0.155989i | \(-0.0498564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 297.000 | 0.822715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −49.0000 | − | 343.000i | −0.134247 | − | 0.939726i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −377.000 | − | 377.000i | −1.02725 | − | 1.02725i | −0.999618 | − | 0.0276297i | \(-0.991204\pi\) |
−0.0276297 | − | 0.999618i | \(-0.508796\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 98.0000 | 0.264151 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 217.000 | − | 217.000i | 0.581769 | − | 0.581769i | −0.353620 | − | 0.935389i | \(-0.615049\pi\) |
0.935389 | + | 0.353620i | \(0.115049\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 72.0000 | + | 72.0000i | 0.190981 | + | 0.190981i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 56.0000i | 0.147757i | 0.997267 | + | 0.0738786i | \(0.0235377\pi\) | ||||
−0.997267 | + | 0.0738786i | \(0.976462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 57.0000 | − | 57.0000i | 0.148825 | − | 0.148825i | −0.628768 | − | 0.777593i | \(-0.716440\pi\) |
0.777593 | + | 0.628768i | \(0.216440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 490.000 | − | 70.0000i | 1.27273 | − | 0.181818i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 312.000i | 0.802057i | 0.916066 | + | 0.401028i | \(0.131347\pi\) | ||||
−0.916066 | + | 0.401028i | \(0.868653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 46.0000 | 0.117647 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −384.000 | − | 288.000i | −0.972152 | − | 0.729114i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 193.000 | + | 193.000i | 0.486146 | + | 0.486146i | 0.907088 | − | 0.420942i | \(-0.138300\pi\) |
−0.420942 | + | 0.907088i | \(0.638300\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 0.0748130 | 0.0374065 | − | 0.999300i | \(-0.488090\pi\) | ||||
0.0374065 | + | 0.999300i | \(0.488090\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 126.000 | − | 126.000i | 0.312655 | − | 0.312655i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 330.000 | + | 330.000i | 0.810811 | + | 0.810811i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 432.000i | 1.05623i | 0.849171 | + | 0.528117i | \(0.177102\pi\) | ||||
−0.849171 | + | 0.528117i | \(0.822898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 392.000 | − | 392.000i | 0.949153 | − | 0.949153i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 63.0000 | + | 441.000i | 0.151807 | + | 1.06265i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 168.000i | − | 0.400955i | −0.979698 | − | 0.200477i | \(-0.935751\pi\) | ||
0.979698 | − | 0.200477i | \(-0.0642493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −454.000 | −1.07838 | −0.539192 | − | 0.842183i | \(-0.681270\pi\) | ||||
−0.539192 | + | 0.842183i | \(0.681270\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.0000 | + | 31.0000i | −0.0400000 | + | 0.0729412i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 294.000 | + | 294.000i | 0.688525 | + | 0.688525i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −494.000 | −1.14617 | −0.573086 | − | 0.819495i | \(-0.694254\pi\) | ||||
−0.573086 | + | 0.819495i | \(0.694254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −511.000 | + | 511.000i | −1.18014 | + | 1.18014i | −0.200431 | + | 0.979708i | \(0.564234\pi\) |
−0.979708 | + | 0.200431i | \(0.935766\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −184.000 | − | 184.000i | −0.421053 | − | 0.421053i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 176.000i | − | 0.400911i | −0.979703 | − | 0.200456i | \(-0.935758\pi\) | ||
0.979703 | − | 0.200456i | \(-0.0642422\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 177.000 | − | 177.000i | 0.399549 | − | 0.399549i | −0.478525 | − | 0.878074i | \(-0.658828\pi\) |
0.878074 | + | 0.478525i | \(0.158828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 448.000 | + | 336.000i | 1.00674 | + | 0.755056i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 608.000i | 1.35412i | 0.735928 | + | 0.677060i | \(0.236746\pi\) | ||||
−0.735928 | + | 0.677060i | \(0.763254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 140.000 | 0.310421 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 378.000 | − | 504.000i | 0.830769 | − | 1.10769i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 609.000 | + | 609.000i | 1.33260 | + | 1.33260i | 0.903033 | + | 0.429571i | \(0.141335\pi\) |
0.429571 | + | 0.903033i | \(0.358665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −490.000 | −1.06291 | −0.531453 | − | 0.847088i | \(-0.678354\pi\) | ||||
−0.531453 | + | 0.847088i | \(0.678354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.00000 | − | 7.00000i | 0.0151188 | − | 0.0151188i | −0.699507 | − | 0.714626i | \(-0.746597\pi\) |
0.714626 | + | 0.699507i | \(0.246597\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.0000 | + | 25.0000i | 0.0535332 | + | 0.0535332i | 0.733367 | − | 0.679833i | \(-0.237948\pi\) |
−0.679833 | + | 0.733367i | \(0.737948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 98.0000i | 0.208955i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 150.000 | − | 150.000i | 0.317125 | − | 0.317125i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 192.000 | − | 56.0000i | 0.404211 | − | 0.117895i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 128.000i | − | 0.267223i | −0.991034 | − | 0.133612i | \(-0.957343\pi\) | ||
0.991034 | − | 0.133612i | \(-0.0426575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 594.000 | 1.23493 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 231.000 | − | 33.0000i | 0.476289 | − | 0.0680412i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −249.000 | − | 249.000i | −0.511294 | − | 0.511294i | 0.403629 | − | 0.914923i | \(-0.367749\pi\) |
−0.914923 | + | 0.403629i | \(0.867749\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 650.000 | 1.32383 | 0.661914 | − | 0.749579i | \(-0.269744\pi\) | ||||
0.661914 | + | 0.749579i | \(0.269744\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000 | − | 8.00000i | 0.0162272 | − | 0.0162272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 686.000 | + | 686.000i | 1.38028 | + | 1.38028i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 632.000i | − | 1.26653i | −0.773934 | − | 0.633267i | \(-0.781714\pi\) | ||
0.773934 | − | 0.633267i | \(-0.218286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −471.000 | + | 471.000i | −0.936382 | + | 0.936382i | −0.998094 | − | 0.0617123i | \(-0.980344\pi\) |
0.0617123 | + | 0.998094i | \(0.480344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −78.0000 | + | 104.000i | −0.154455 | + | 0.205941i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.00000i | 0.0157171i | 0.999969 | + | 0.00785855i | \(0.00250148\pi\) | ||||
−0.999969 | + | 0.00785855i | \(0.997499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 686.000 | 1.34247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 73.0000 | + | 511.000i | 0.141748 | + | 0.992233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −390.000 | − | 390.000i | −0.754352 | − | 0.754352i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 366.000 | 0.702495 | 0.351248 | − | 0.936283i | \(-0.385758\pi\) | ||||
0.351248 | + | 0.936283i | \(0.385758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −273.000 | + | 273.000i | −0.521989 | + | 0.521989i | −0.918172 | − | 0.396183i | \(-0.870335\pi\) |
0.396183 | + | 0.918172i | \(0.370335\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.0000 | − | 14.0000i | −0.0265655 | − | 0.0265655i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 529.000i | − | 1.00000i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 126.000 | − | 126.000i | 0.236398 | − | 0.236398i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 847.000 | − | 121.000i | 1.58318 | − | 0.226168i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 490.000i | 0.909091i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 394.000 | 0.728281 | 0.364140 | − | 0.931344i | \(-0.381363\pi\) | ||||
0.364140 | + | 0.931344i | \(0.381363\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −544.000 | − | 408.000i | −0.998165 | − | 0.748624i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 231.000 | + | 231.000i | 0.422303 | + | 0.422303i | 0.885996 | − | 0.463693i | \(-0.153476\pi\) |
−0.463693 | + | 0.885996i | \(0.653476\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −64.0000 | −0.116152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 672.000 | − | 672.000i | 1.21519 | − | 1.21519i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 735.000 | + | 735.000i | 1.31957 | + | 1.31957i | 0.914116 | + | 0.405453i | \(0.132886\pi\) |
0.405453 | + | 0.914116i | \(0.367114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 270.000i | − | 0.483005i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 609.000 | − | 609.000i | 1.08171 | − | 1.08171i | 0.0853545 | − | 0.996351i | \(-0.472798\pi\) |
0.996351 | − | 0.0853545i | \(-0.0272023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −127.000 | − | 889.000i | −0.224779 | − | 1.57345i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 560.000i | − | 0.984183i | −0.870544 | − | 0.492091i | \(-0.836233\pi\) | ||
0.870544 | − | 0.492091i | \(-0.163767\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −938.000 | −1.64273 | −0.821366 | − | 0.570401i | \(-0.806788\pi\) | ||||
−0.821366 | + | 0.570401i | \(0.806788\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 713.000 | + | 391.000i | 1.24000 | + | 0.680000i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 97.0000 | + | 97.0000i | 0.168111 | + | 0.168111i | 0.786149 | − | 0.618038i | \(-0.212072\pi\) |
−0.618038 | + | 0.786149i | \(0.712072\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −882.000 | −1.51807 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 70.0000 | − | 70.0000i | 0.120069 | − | 0.120069i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.0000 | − | 39.0000i | −0.0664395 | − | 0.0664395i | 0.673106 | − | 0.739546i | \(-0.264960\pi\) |
−0.739546 | + | 0.673106i | \(0.764960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 112.000i | 0.190153i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 479.000 | − | 479.000i | 0.807757 | − | 0.807757i | −0.176537 | − | 0.984294i | \(-0.556489\pi\) |
0.984294 | + | 0.176537i | \(0.0564895\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −56.0000 | − | 42.0000i | −0.0941176 | − | 0.0705882i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1040.00i | − | 1.73623i | −0.496366 | − | 0.868114i | \(-0.665332\pi\) | ||
0.496366 | − | 0.868114i | \(-0.334668\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −430.000 | −0.715474 | −0.357737 | − | 0.933822i | \(-0.616452\pi\) | ||||
−0.357737 | + | 0.933822i | \(0.616452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −63.0000 | + | 84.0000i | −0.104132 | + | 0.138843i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 423.000 | + | 423.000i | 0.696870 | + | 0.696870i | 0.963734 | − | 0.266864i | \(-0.0859875\pi\) |
−0.266864 | + | 0.963734i | \(0.585988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −702.000 | −1.14894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 249.000 | − | 249.000i | 0.406199 | − | 0.406199i | −0.474212 | − | 0.880411i | \(-0.657267\pi\) |
0.880411 | + | 0.474212i | \(0.157267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −321.000 | − | 321.000i | −0.520259 | − | 0.520259i | 0.397390 | − | 0.917650i | \(-0.369916\pi\) |
−0.917650 | + | 0.397390i | \(0.869916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 600.000i | 0.969305i | 0.874707 | + | 0.484653i | \(0.161054\pi\) | ||||
−0.874707 | + | 0.484653i | \(0.838946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −784.000 | + | 784.000i | −1.25843 | + | 1.25843i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −527.000 | + | 336.000i | −0.843200 | + | 0.537600i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 66.0000i | − | 0.104928i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 638.000 | 1.01109 | 0.505547 | − | 0.862799i | \(-0.331291\pi\) | ||||
0.505547 | + | 0.862799i | \(0.331291\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 49.0000 | − | 7.00000i | 0.0771654 | − | 0.0110236i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 441.000 | + | 441.000i | 0.692308 | + | 0.692308i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −482.000 | −0.751950 | −0.375975 | − | 0.926630i | \(-0.622692\pi\) | ||||
−0.375975 | + | 0.926630i | \(0.622692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.0000 | + | 33.0000i | −0.0513219 | + | 0.0513219i | −0.732302 | − | 0.680980i | \(-0.761554\pi\) |
0.680980 | + | 0.732302i | \(0.261554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.00000 | − | 7.00000i | −0.0108192 | − | 0.0108192i | 0.701677 | − | 0.712496i | \(-0.252435\pi\) |
−0.712496 | + | 0.701677i | \(0.752435\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 560.000i | − | 0.862866i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 471.000 | − | 471.000i | 0.721286 | − | 0.721286i | −0.247581 | − | 0.968867i | \(-0.579636\pi\) |
0.968867 | + | 0.247581i | \(0.0796356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −690.000 | + | 920.000i | −1.05344 | + | 1.40458i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 328.000i | − | 0.497724i | −0.968539 | − | 0.248862i | \(-0.919943\pi\) | ||
0.968539 | − | 0.248862i | \(-0.0800565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −742.000 | −1.12254 | −0.561271 | − | 0.827632i | \(-0.689687\pi\) | ||||
−0.561271 | + | 0.827632i | \(0.689687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 56.0000 | + | 392.000i | 0.0842105 | + | 0.589474i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −184.000 | − | 184.000i | −0.275862 | − | 0.275862i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 420.000 | 0.625931 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −287.000 | + | 287.000i | −0.426449 | + | 0.426449i | −0.887417 | − | 0.460968i | \(-0.847502\pi\) |
0.460968 | + | 0.887417i | \(0.347502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −577.000 | − | 577.000i | −0.852290 | − | 0.852290i | 0.138125 | − | 0.990415i | \(-0.455892\pi\) |
−0.990415 | + | 0.138125i | \(0.955892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 462.000i | 0.680412i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −399.000 | + | 399.000i | −0.584187 | + | 0.584187i | −0.936051 | − | 0.351864i | \(-0.885548\pi\) |
0.351864 | + | 0.936051i | \(0.385548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 441.000 | − | 63.0000i | 0.643796 | − | 0.0919708i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 126.000i | − | 0.182874i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −378.000 | −0.547033 | −0.273517 | − | 0.961867i | \(-0.588187\pi\) | ||||
−0.273517 | + | 0.961867i | \(0.588187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 352.000 | + | 264.000i | 0.506475 | + | 0.379856i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0000 | − | 14.0000i | −0.0200861 | − | 0.0200861i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 470.000 | 0.670471 | 0.335235 | − | 0.942134i | \(-0.391184\pi\) | ||||
0.335235 | + | 0.942134i | \(0.391184\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −264.000 | + | 264.000i | −0.375533 | + | 0.375533i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −182.000 | − | 182.000i | −0.257426 | − | 0.257426i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1192.00i | 1.68124i | 0.541624 | + | 0.840621i | \(0.317810\pi\) | ||||
−0.541624 | + | 0.840621i | \(0.682190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −322.000 | + | 322.000i | −0.451613 | + | 0.451613i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −90.0000 | − | 630.000i | −0.125874 | − | 0.881119i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 608.000i | − | 0.845619i | −0.906219 | − | 0.422809i | \(-0.861044\pi\) | ||
0.906219 | − | 0.422809i | \(-0.138956\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1022.00 | −1.41748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 192.000 | − | 56.0000i | 0.264828 | − | 0.0772414i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −441.000 | − | 441.000i | −0.606602 | − | 0.606602i | 0.335454 | − | 0.942057i | \(-0.391110\pi\) |
−0.942057 | + | 0.335454i | \(0.891110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.0000 | −0.0410397 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 361.000 | − | 361.000i | 0.492497 | − | 0.492497i | −0.416595 | − | 0.909092i | \(-0.636777\pi\) |
0.909092 | + | 0.416595i | \(0.136777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 70.0000 | + | 70.0000i | 0.0949796 | + | 0.0949796i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 920.000i | − | 1.24493i | −0.782649 | − | 0.622463i | \(-0.786132\pi\) | ||
0.782649 | − | 0.622463i | \(-0.213868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −343.000 | + | 343.000i | −0.461642 | + | 0.461642i | −0.899193 | − | 0.437551i | \(-0.855846\pi\) |
0.437551 | + | 0.899193i | \(0.355846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −672.000 | − | 504.000i | −0.902013 | − | 0.676510i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1694.00i | 2.26168i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −786.000 | −1.04660 | −0.523302 | − | 0.852147i | \(-0.675300\pi\) | ||||
−0.523302 | + | 0.852147i | \(0.675300\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −390.000 | + | 520.000i | −0.516556 | + | 0.688742i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −63.0000 | − | 63.0000i | −0.0832232 | − | 0.0832232i | 0.664270 | − | 0.747493i | \(-0.268743\pi\) |
−0.747493 | + | 0.664270i | \(0.768743\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 398.000 | 0.522996 | 0.261498 | − | 0.965204i | \(-0.415784\pi\) | ||||
0.261498 | + | 0.965204i | \(0.415784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 952.000 | − | 952.000i | 1.24771 | − | 1.24771i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −504.000 | − | 504.000i | −0.657106 | − | 0.657106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 704.000i | 0.915475i | 0.889087 | + | 0.457737i | \(0.151340\pi\) | ||||
−0.889087 | + | 0.457737i | \(0.848660\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −825.000 | + | 825.000i | −1.06727 | + | 1.06727i | −0.0697026 | + | 0.997568i | \(0.522205\pi\) |
−0.997568 | + | 0.0697026i | \(0.977795\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −98.0000 | − | 336.000i | −0.126452 | − | 0.433548i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 112.000i | 0.143774i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 980.000 | 1.25480 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −441.000 | + | 63.0000i | −0.561783 | + | 0.0802548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 71.0000 | + | 71.0000i | 0.0902160 | + | 0.0902160i | 0.750775 | − | 0.660559i | \(-0.229680\pi\) |
−0.660559 | + | 0.750775i | \(0.729680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1778.00 | 2.24779 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 378.000 | − | 378.000i | 0.476671 | − | 0.476671i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.0000 | − | 33.0000i | −0.0414053 | − | 0.0414053i | 0.686101 | − | 0.727506i | \(-0.259321\pi\) |
−0.727506 | + | 0.686101i | \(0.759321\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 78.0000i | 0.0976220i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 490.000 | − | 490.000i | 0.610212 | − | 0.610212i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −966.000 | + | 1288.00i | −1.20000 | + | 1.60000i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 368.000i | − | 0.454883i | −0.973792 | − | 0.227441i | \(-0.926964\pi\) | ||
0.973792 | − | 0.227441i | \(-0.0730360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 886.000 | 1.09248 | 0.546239 | − | 0.837629i | \(-0.316059\pi\) | ||||
0.546239 | + | 0.837629i | \(0.316059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 65.0000 | + | 455.000i | 0.0797546 | + | 0.558282i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 120.000 | + | 120.000i | 0.146879 | + | 0.146879i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 614.000 | 0.747868 | 0.373934 | − | 0.927455i | \(-0.378009\pi\) | ||||
0.373934 | + | 0.927455i | \(0.378009\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1001.00 | + | 1001.00i | −1.21628 | + | 1.21628i | −0.247358 | + | 0.968924i | \(0.579562\pi\) |
−0.968924 | + | 0.247358i | \(0.920438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −615.000 | − | 615.000i | −0.743652 | − | 0.743652i | 0.229627 | − | 0.973279i | \(-0.426249\pi\) |
−0.973279 | + | 0.229627i | \(0.926249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 616.000i | − | 0.743064i | −0.928420 | − | 0.371532i | \(-0.878833\pi\) | ||
0.928420 | − | 0.371532i | \(-0.121167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49.0000 | − | 49.0000i | 0.0588235 | − | 0.0588235i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −721.000 | + | 103.000i | −0.863473 | + | 0.123353i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1424.00i | 1.69726i | 0.528988 | + | 0.848629i | \(0.322572\pi\) | ||||
−0.528988 | + | 0.848629i | \(0.677428\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 777.000 | 0.923900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.0000 | + | 21.0000i | 0.0331361 | + | 0.0248521i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −147.000 | − | 147.000i | −0.173554 | − | 0.173554i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1518.00 | −1.78378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −935.000 | + | 935.000i | −1.09613 | + | 1.09613i | −0.101273 | + | 0.994859i | \(0.532291\pi\) |
−0.994859 | + | 0.101273i | \(0.967709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 63.0000 | + | 63.0000i | 0.0735123 | + | 0.0735123i | 0.742907 | − | 0.669395i | \(-0.233446\pi\) |
−0.669395 | + | 0.742907i | \(0.733446\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 392.000i | − | 0.456345i | −0.973621 | − | 0.228172i | \(-0.926725\pi\) | ||
0.973621 | − | 0.228172i | \(-0.0732749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 217.000 | − | 217.000i | 0.251448 | − | 0.251448i | −0.570116 | − | 0.821564i | \(-0.693102\pi\) |
0.821564 | + | 0.570116i | \(0.193102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73.0000 | + | 511.000i | 0.0843931 | + | 0.590751i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 960.000i | − | 1.10472i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 126.000 | 0.144661 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −511.000 | − | 1127.00i | −0.584000 | − | 1.28800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −831.000 | − | 831.000i | −0.947548 | − | 0.947548i | 0.0511429 | − | 0.998691i | \(-0.483714\pi\) |
−0.998691 | + | 0.0511429i | \(0.983714\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −322.000 | −0.365494 | −0.182747 | − | 0.983160i | \(-0.558499\pi\) | ||||
−0.182747 | + | 0.983160i | \(0.558499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 287.000 | − | 287.000i | 0.325028 | − | 0.325028i | −0.525664 | − | 0.850692i | \(-0.676183\pi\) |
0.850692 | + | 0.525664i | \(0.176183\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −903.000 | − | 903.000i | −1.01804 | − | 1.01804i | −0.999834 | − | 0.0182040i | \(-0.994205\pi\) |
−0.0182040 | − | 0.999834i | \(-0.505795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 98.0000i | 0.110236i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 312.000 | − | 312.000i | 0.349384 | − | 0.349384i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 224.000 | + | 168.000i | 0.250279 | + | 0.187709i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 112.000i | 0.124583i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.0000 | −0.0155383 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −210.000 | + | 280.000i | −0.232044 | + | 0.309392i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1081.00 | − | 1081.00i | −1.19184 | − | 1.19184i | −0.976550 | − | 0.215291i | \(-0.930930\pi\) |
−0.215291 | − | 0.976550i | \(-0.569070\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −238.000 | −0.261251 | −0.130626 | − | 0.991432i | \(-0.541699\pi\) | ||||
−0.130626 | + | 0.991432i | \(0.541699\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −630.000 | + | 630.000i | −0.690033 | + | 0.690033i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1610.00 | − | 1610.00i | −1.75573 | − | 1.75573i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1552.00i | 1.68879i | 0.535719 | + | 0.844396i | \(0.320040\pi\) | ||||
−0.535719 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 882.000 | − | 882.000i | 0.955580 | − | 0.955580i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 561.000 | − | 1023.00i | 0.606486 | − | 1.10595i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 224.000i | 0.241119i | 0.992706 | + | 0.120560i | \(0.0384689\pi\) | ||||
−0.992706 | + | 0.120560i | \(0.961531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −392.000 | −0.421053 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −70.0000 | + | 10.0000i | −0.0748663 | + | 0.0106952i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −383.000 | − | 383.000i | −0.408751 | − | 0.408751i | 0.472552 | − | 0.881303i | \(-0.343333\pi\) |
−0.881303 | + | 0.472552i | \(0.843333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0000 | −0.0446334 | −0.0223167 | − | 0.999751i | \(-0.507104\pi\) | ||||
−0.0223167 | + | 0.999751i | \(0.507104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −322.000 | + | 322.000i | −0.341463 | + | 0.341463i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1337.00 | + | 1337.00i | 1.41183 | + | 1.41183i | 0.746977 | + | 0.664849i | \(0.231504\pi\) |
0.664849 | + | 0.746977i | \(0.268496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 882.000i | − | 0.929399i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −273.000 | + | 273.000i | −0.286464 | + | 0.286464i | −0.835680 | − | 0.549216i | \(-0.814926\pi\) |
0.549216 | + | 0.835680i | \(0.314926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −426.000 | + | 568.000i | −0.446073 | + | 0.594764i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 882.000i | 0.919708i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −765.000 | −0.796046 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 63.0000 | + | 441.000i | 0.0652850 | + | 0.456995i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 743.000 | + | 743.000i | 0.768356 | + | 0.768356i | 0.977817 | − | 0.209461i | \(-0.0671710\pi\) |
−0.209461 | + | 0.977817i | \(0.567171\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 266.000 | 0.273944 | 0.136972 | − | 0.990575i | \(-0.456263\pi\) | ||||
0.136972 | + | 0.990575i | \(0.456263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −616.000 | + | 616.000i | −0.633094 | + | 0.633094i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −417.000 | − | 417.000i | −0.426817 | − | 0.426817i | 0.460726 | − | 0.887543i | \(-0.347589\pi\) |
−0.887543 | + | 0.460726i | \(0.847589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1120.00i | 1.14402i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −631.000 | + | 631.000i | −0.641913 | + | 0.641913i | −0.951025 | − | 0.309113i | \(-0.899968\pi\) |
0.309113 | + | 0.951025i | \(0.399968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 441.000 | − | 63.0000i | 0.447716 | − | 0.0639594i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 690.000i | 0.697674i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0000 | 0.0141271 | 0.00706357 | − | 0.999975i | \(-0.497752\pi\) | ||||
0.00706357 | + | 0.999975i | \(0.497752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1344.00 | − | 1008.00i | −1.35075 | − | 1.01307i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −671.000 | − | 671.000i | −0.673019 | − | 0.673019i | 0.285392 | − | 0.958411i | \(-0.407876\pi\) |
−0.958411 | + | 0.285392i | \(0.907876\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.3.bh.e.577.1 | 2 | ||
3.2 | odd | 2 | 80.3.p.a.17.1 | 2 | |||
4.3 | odd | 2 | 180.3.l.a.37.1 | 2 | |||
5.3 | odd | 4 | inner | 720.3.bh.e.433.1 | 2 | ||
12.11 | even | 2 | 20.3.f.a.17.1 | yes | 2 | ||
15.2 | even | 4 | 400.3.p.d.193.1 | 2 | |||
15.8 | even | 4 | 80.3.p.a.33.1 | 2 | |||
15.14 | odd | 2 | 400.3.p.d.257.1 | 2 | |||
20.3 | even | 4 | 180.3.l.a.73.1 | 2 | |||
20.7 | even | 4 | 900.3.l.a.793.1 | 2 | |||
20.19 | odd | 2 | 900.3.l.a.757.1 | 2 | |||
24.5 | odd | 2 | 320.3.p.g.257.1 | 2 | |||
24.11 | even | 2 | 320.3.p.c.257.1 | 2 | |||
60.23 | odd | 4 | 20.3.f.a.13.1 | ✓ | 2 | ||
60.47 | odd | 4 | 100.3.f.a.93.1 | 2 | |||
60.59 | even | 2 | 100.3.f.a.57.1 | 2 | |||
84.83 | odd | 2 | 980.3.l.a.197.1 | 2 | |||
120.53 | even | 4 | 320.3.p.g.193.1 | 2 | |||
120.83 | odd | 4 | 320.3.p.c.193.1 | 2 | |||
420.83 | even | 4 | 980.3.l.a.393.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.3.f.a.13.1 | ✓ | 2 | 60.23 | odd | 4 | ||
20.3.f.a.17.1 | yes | 2 | 12.11 | even | 2 | ||
80.3.p.a.17.1 | 2 | 3.2 | odd | 2 | |||
80.3.p.a.33.1 | 2 | 15.8 | even | 4 | |||
100.3.f.a.57.1 | 2 | 60.59 | even | 2 | |||
100.3.f.a.93.1 | 2 | 60.47 | odd | 4 | |||
180.3.l.a.37.1 | 2 | 4.3 | odd | 2 | |||
180.3.l.a.73.1 | 2 | 20.3 | even | 4 | |||
320.3.p.c.193.1 | 2 | 120.83 | odd | 4 | |||
320.3.p.c.257.1 | 2 | 24.11 | even | 2 | |||
320.3.p.g.193.1 | 2 | 120.53 | even | 4 | |||
320.3.p.g.257.1 | 2 | 24.5 | odd | 2 | |||
400.3.p.d.193.1 | 2 | 15.2 | even | 4 | |||
400.3.p.d.257.1 | 2 | 15.14 | odd | 2 | |||
720.3.bh.e.433.1 | 2 | 5.3 | odd | 4 | inner | ||
720.3.bh.e.577.1 | 2 | 1.1 | even | 1 | trivial | ||
900.3.l.a.757.1 | 2 | 20.19 | odd | 2 | |||
900.3.l.a.793.1 | 2 | 20.7 | even | 4 | |||
980.3.l.a.197.1 | 2 | 84.83 | odd | 2 | |||
980.3.l.a.393.1 | 2 | 420.83 | even | 4 |